Multielectron methods

Current Situation and Future Development of Discrete Variational Multielectron Method... 

We recently developed a general method, to directly calculate the electronic stracture in many-electron system DV-ME (Discrete Variational MultiElectron) method. The first apphcation of this method has been reported by Ogasawara et al. in ruby crystal (17). They clarified the effects of covalency and trigonal distortion of impurity-state wave functions on the multiplet structure. 

During the meeting, various applications of and perspectives on the DV-Xa method were discussed in detail. Among them, the usefulness of theoretical analysis using DV-Xa calculation for X-ray and electron spectroscopy such as XPS, XES (X-ray emission spectroscopy), XANES, ELNES, and AES was presented and discussed. A new universal computational method for the many-electron-state, DV-ME (DV-multielectron) method was introduced by demonstrating its advantages and possibilities for application to the calculation of the multiplet structure of the d-d transition in various transition metal oxides. Another topic was the application of the DV-Xa method to materials science. The study of... 

Quantum mechanics describes molecules in terms of interactions between nuclei and electrons and molecular geometry in terms of minimum energy arrangements of nuclei. All quantum-mechanical methods ultimately trace back to Schrodinger s (time-independent) equation, which may be solved exactly for the hydrogen atom. For a multinuclear and multielectron system, the Schrodinger equation may be defined as ... 

Invited 1. Kazuyoshi Ogasawara (Kwansei Gakuin University) Current Situation and Future Development of Discrete Variational Multielectron (DVME) Method... 

The greater the number of functions 4 J, belonging to the orthonormal set, the more completely and in more detail the spectrum of the /(-decay-induced excitations of a molecule can be calculated. Consequently, the method for calculating the wave functions of the daughter ion must be such that at a reasonable volume of calculation we would be able to construct a sufficiently large number of multielectron wave functions of excited states. The Hartree Fock method allows one to construct the wave functions of excited states as the combinations of determinants symmetrized in a certain way. Within this method the excitation is considered to be a transition of an electron from an occupied Hartree-Fock molecular orbital into a vacant one. 

Thus, as an MO basis for constructing the multielectron wave functions of configurations given by Eq. (33), we will use the Hartree-Fock MO for the occupied one-electron states and the Huzinaga MO [Eq. (34)] for the excited ones. An advantage of the Huzinaga MOs is the simplicity of the way they are obtained, since Eq. (34) is an equation with constant coefficients and one does not have to use the iteration method. Moreover, when one uses the Huzinaga... 

The equation is used to describe the behaviour of an atom or molecule in terms of its wave-like (or quantum) nature. By trying to solve the equation the energy levels of the system are calculated. However, the complex nature of multielectron/nuclei systems is simplified using the Born-Oppenheimer approximation. Unfortunately it is not possible to obtain an exact solution of the Schrddinger wave equation except for the simplest case, i.e. hydrogen. Theoretical chemists have therefore established approaches to find approximate solutions to the wave equation. One such approach uses the Hartree-Fock self-consistent field method, although other approaches are possible. Two important classes of calculation are based on ab initio or semi-empirical methods. Ah initio literally means from the beginning . The term is used in computational chemistry to describe computations which are not based upon any experimental data, but based purely on theoretical principles. This is not to say that this approach has no scientific basis - indeed the approach uses mathematical approximations to simplify, for example, a differential equation. In contrast, semi-empirical methods utilize some experimental data to simplify the calculations. As a consequence semi-empirical methods are more rapid than ab initio. 

Several excellent reviews and books have been written on the two main first principles techniques. The standard ab initio, which try to solve directly the Schrodinger equation using a multielectron wavefimction approach, and the DFT methods in which instead of the many-electron wavefimction a non-interactive wavefimction is calculated fi om which the electron density is... 

The basis of computational quantum mechanics is the equation posed by Erwin Schrbdinger in 1925 that bears his name. Solving this equation for multielectron systems remains as the central problem of computational quantum mechanics. The difficulty is that because of the interactions, the wave function of each electron in a molecule is affected by, and coupled to, the wave functions of all other electrons, requiring a computationally intense self-consistent iterative calculation. As computational equipment and methods have improved, quantum chemical calculations have become more accurate, and the molecules to which they have been applied more complex, now even including proteins and other biomolecules. 

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